Council tax is a property tax. How much you pay is based on where you live (i.e. in which borough), the value of your home and who lives in it. As a student, you may be exempt or pay less tax depending on your situation.
Students in a full-time course and attend classes 21 hours a week for a minimum of 24 weeks a year may get a reduction, as do students who are under 20 years old, and studying a course not above A levels, ONC or OND. But don't forget to get a certificate from your uni/college proving that you are a full-time student; you could be asked to forward this on to your local council.
If you live with someone who is not a student, you may still be able to get a single-person discount of about 25%.
However, you may not have to pay any council tax at if you live in a halls of residence (as long as there are only students living there), or if you live in a private flat where everyone is studying full time.
To make sure you don't pay taxes you are exempt from or have a landlord who tries it on to get more of your precious beer money, contact your local council for accurate up to date information on your situation.